Three blocks of masses $m_1, m_2$ and $m_3$ are connected by massless strings as shown on a frictionless table. They are pulled with a force $F = 40 \, N$. If $m_1 = 10 \, kg, m_2 = 6 \, kg$ and $m_3 = 4 \, kg$,the tension $T_2$ (between $m_1$ and $m_2$) will be ........ $N$.

Two blocks $A$ and $B$ of mass $m$ and $2m$ respectively are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. The spring is stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length is:

$A$ system containing masses and pulleys connected on an inclined plane is shown in the figure. If the system is in equilibrium, then the value of $m$ is (in $\,kg$)

The figure shows three blocks in contact and kept on a smooth horizontal surface. What is the ratio of the force exerted by block $A$ on $B$ to that of $B$ on $C$?

$A$ horizontal force of $10 \,N$ is applied to a block $A$ as shown in the figure. The masses of blocks $A$ and $B$ are $2 \,kg$ and $3 \,kg$ respectively. The blocks slide over a frictionless surface. The force exerted by block $A$ on block $B$ is:

$A$ block of mass $M$ on a horizontal smooth surface is pulled by a load of mass $M/2$ by means of a rope $AB$ and string $BC$ as shown in the figure. The length and mass of the rope $AB$ are $L$ and $M/2$ respectively. As the block is pulled from $AB = L$ to $AB = 0$,its acceleration changes from: